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Journal Articles Stochastic Processes and their Applications Year : 2013

## Optimal stopping for partially observed piecewise-deterministic Markov processes

• Function : Author
Benoîte de Saporta
François Dufour

#### Abstract

This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of the partially observed optimal stopping problem. Then, we propose a numerical method, based on the quantization of the discrete-time filter process and the inter-jump times, to approximate the value function and to compute an actual $\epsilon$-optimal stopping time. We prove the convergence of the algorithms and bound the rates of convergence.

#### Domains

Mathematics [math] Probability [math.PR]

### Dates and versions

hal-00755052 , version 1 (20-11-2012)

### Identifiers

• HAL Id : hal-00755052 , version 1
• ARXIV :
• DOI :

### Cite

Adrien Brandejsky, Benoîte de Saporta, François Dufour. Optimal stopping for partially observed piecewise-deterministic Markov processes. Stochastic Processes and their Applications, 2013, 123, pp.3201-3238. ⟨10.1016/j.spa.2013.03.006⟩. ⟨hal-00755052⟩

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